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Swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field

Zhang Guo-Feng Xing Zhao

Swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field

Zhang Guo-Feng, Xing Zhao
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  • Spin model plays an important role in the realization of quantum information processing. Quantum entanglement can be constructed, also (swap)n quantum logic gate is available if anisotropy is ignored, when Heisenberg interaction between spins is used; thus a complete quantum computing gate will be realized by combining single-qubit rotation gate. To study the influence of anisotropy on logic gate has high academic value since anisotropy is inevitable in any solid material. In this paper, swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field is discussed. The swap errors caused by the anisotropy parameter ν of the exchange interaction between spins and the inhomogeneous field δ are evaluated. We can see clearly when the swap operation can be approximately used as an ideal swap gate.
    • Funds:
    [1]

    [1]Brassard G, Braunstein S L, Cleve R 1998 Physica D 120 43

    [2]

    [2]Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120

    [3]

    [3]Zhang G F, Li S S 2006 Optics Communications 260 347 Zhang G F, Li S S 2006 Eur. Phys. J. D 37 123

    [4]

    [4]Cai Z, Lu W B, Liu Y J 2008 Acta. Phys. Sin. 57 7267(in Chinese)[蔡桌、陆文彬、刘拥军 2008 物理学报 57 7267]

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    [5]Qin M, Tian D P, Tao Y J 2008 Acta. Phys. Sin. 57 5395(in Chinese)[秦猛、田东平、陶应娟 2008 物理学报 57 5395]

    [6]

    [6]Shan C J, Chen W W, Liu T K, Huang Y X, Li H 2008 Chin. Phys. B 17 4002

    [7]

    [7]Huang L Y, Fang M F 2008 Chin. Phys. B 17 2339

    [8]

    [8]Xi X Q, Liu W M 2007 Chin. Phys. 16 1858

    [9]

    [9]Zhang G F 2007 J. Phys.: Cond. Matter 19 456205

    [10]

    [10]Zhou Y, Zhang G F, Yang F H, Feng S L 2007 Phys. Rev. A 75 062304

    [11]

    [11]Yan X B, Wang S J 2006 Acta. Phys. Sin. 55 1591(in Chinese)[严晓波、王顺金 2006 物理学报 55 1591]

    [12]

    [12]Zhang G F, Li S S 2005 Phys. Rev. A 72 034302

  • [1]

    [1]Brassard G, Braunstein S L, Cleve R 1998 Physica D 120 43

    [2]

    [2]Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120

    [3]

    [3]Zhang G F, Li S S 2006 Optics Communications 260 347 Zhang G F, Li S S 2006 Eur. Phys. J. D 37 123

    [4]

    [4]Cai Z, Lu W B, Liu Y J 2008 Acta. Phys. Sin. 57 7267(in Chinese)[蔡桌、陆文彬、刘拥军 2008 物理学报 57 7267]

    [5]

    [5]Qin M, Tian D P, Tao Y J 2008 Acta. Phys. Sin. 57 5395(in Chinese)[秦猛、田东平、陶应娟 2008 物理学报 57 5395]

    [6]

    [6]Shan C J, Chen W W, Liu T K, Huang Y X, Li H 2008 Chin. Phys. B 17 4002

    [7]

    [7]Huang L Y, Fang M F 2008 Chin. Phys. B 17 2339

    [8]

    [8]Xi X Q, Liu W M 2007 Chin. Phys. 16 1858

    [9]

    [9]Zhang G F 2007 J. Phys.: Cond. Matter 19 456205

    [10]

    [10]Zhou Y, Zhang G F, Yang F H, Feng S L 2007 Phys. Rev. A 75 062304

    [11]

    [11]Yan X B, Wang S J 2006 Acta. Phys. Sin. 55 1591(in Chinese)[严晓波、王顺金 2006 物理学报 55 1591]

    [12]

    [12]Zhang G F, Li S S 2005 Phys. Rev. A 72 034302

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  • Received Date:  13 June 2009
  • Accepted Date:  18 June 2009
  • Published Online:  15 March 2010

Swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field

  • 1. 北京航空航天大学物理科学与核能工程学院物理系,北京 100191

Abstract: Spin model plays an important role in the realization of quantum information processing. Quantum entanglement can be constructed, also (swap)n quantum logic gate is available if anisotropy is ignored, when Heisenberg interaction between spins is used; thus a complete quantum computing gate will be realized by combining single-qubit rotation gate. To study the influence of anisotropy on logic gate has high academic value since anisotropy is inevitable in any solid material. In this paper, swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field is discussed. The swap errors caused by the anisotropy parameter ν of the exchange interaction between spins and the inhomogeneous field δ are evaluated. We can see clearly when the swap operation can be approximately used as an ideal swap gate.

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